Harmonic Maps Into Trees and Graphs PDF Download

Author: Martin Hesse
Publisher:
ISBN:
Category : Dirichlet forms
Languages : en
Pages : 116

View

Book Description

Author: Christopher Kum Anand
Publisher: CRC Press
ISBN: 9781584880325
Category : Mathematics
Languages : en
Pages : 332

View

Book Description
The subject of harmonic morphisms is relatively new but has attracted a huge worldwide following. Mathematicians, young researchers and distinguished experts came from all corners of the globe to the City of Brest - site of the first, international conference devoted to the fledgling but dynamic field of harmonic morphisms. Harmonic Morphisms, Harmonic Maps, and Related Topics reports the proceedings of that conference, forms the first work primarily devoted to harmonic morphisms, bringing together contributions from the founders of the subject, leading specialists, and experts in other related fields. Starting with "The Beginnings of Harmonic Morphisms," which provides the essential background, the first section includes papers on the stability of harmonic morphisms, global properties, harmonic polynomial morphisms, Bochner technique, f-structures, symplectic harmonic morphisms, and discrete harmonic morphisms. The second section addresses the wider domain of harmonic maps and contains some of the most recent results on harmonic maps and surfaces. The final section highlights the rapidly developing subject of constant mean curvature surfaces. Harmonic Morphisms, Harmonic Maps, and Related Topics offers a coherent, balanced account of this fast-growing subject that furnishes a vital reference for anyone working in the field.

Author: Adam Korǹyi (et al.)
Publisher: American Mathematical Soc.
ISBN: 082180605X
Category : Mathematics
Languages : en
Pages : 194

View

Book Description
This volume presents the proceedings of the workshop "Harmonic Functions on Graphs" held at the Graduate Centre of CUNY in the autumn of 1995. The main papers present material from four minicourses given by leading experts: D. Cartwright, A. Figà-Talamanca, S. Sawyer, and T. Steger. These minicrouses are introductions which gradually progress to deeper and less known branches of the subject. One of the topics treated is buildings, which are discrete analogues of symmetric spaces of arbitrary rank; buildings of rank are trees. Harmonic analysis on buildings is a fairly new and important field of research. One of the minicourses discusses buildings from the combinatorial perspective and another examines them from the p-adic perspective. the third minicourse deals with the connections of trees with p-adic analysis, and the fourth deals with random walks, ie., with the probabilistic side of harmonic functions on trees. The book also contains the extended abstracts of 19 of the 20 lectures given by the participants on their recent results. These abstracts, well detailed and clearly understandable, give a good cross-section of the present state of research in the field.

Author: Sergio Albeverio
Publisher: Springer Science & Business Media
ISBN: 3642196594
Category : Mathematics
Languages : en
Pages : 295

View

Book Description
This monograph treats the theory of Dirichlet forms from a comprehensive point of view, using "nonstandard analysis." Thus, it is close in spirit to the discrete classical formulation of Dirichlet space theory by Beurling and Deny (1958). The discrete infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same methods. This setting has the advantage of being independent of special topological properties of the state space and in this sense is a natural one, valid for both finite- and infinite-dimensional spaces. The present monograph provides a thorough treatment of the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes, and summarizes in an epilogue the model-theoretic genericity of hyperfinite stochastic processes theory.

Author: Russell Lyons
Publisher: Cambridge University Press
ISBN: 1316785335
Category : Mathematics
Languages : en
Pages : 1023

View

Book Description
Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

Author: Pavel Exner
Publisher: American Mathematical Soc.
ISBN: 0821844717
Category : Mathematics
Languages : en
Pages : 721

View

Book Description
This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.

Author: Athanase Papadopoulos
Publisher: European Mathematical Society
ISBN: 9783037190296
Category : Mathematics
Languages : en
Pages : 812

View

Book Description
The Teichmuller space of a surface was introduced by O. Teichmuller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group $G$, most notably $G=\mathrm{PSL}(2,\mathbb{R})$ and $G=\mathrm{PSL}(2,\mathbb{C})$. In the 1980s, there evolved an essentially combinatorial treatment of the Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmuller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject.

Author: Alessandro Figá-Talamanca
Publisher: Cambridge University Press
ISBN: 0521424445
Category : Mathematics
Languages : en
Pages : 165

View

Book Description
These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree. The unitary irreducible representations are classified in three types: a continuous series of spherical representations; two special representations; and a countable series of cuspidal representations as defined by G.I. Ol'shiankii. Several notable subgroups of the full automorphism group are also considered. The theory of spherical functions as eigenvalues of a Laplace (or Hecke) operator on the tree is used to introduce spherical representations and their restrictions to discrete subgroups. This will be an excellent companion for all researchers into harmonic analysis or representation theory.

Author: Matthias Keller
Publisher: Cambridge University Press
ISBN: 1108587380
Category : Mathematics
Languages : en
Pages : 493

View

Book Description
This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.

Author: Donghyun Kim
Publisher: Springer Nature
ISBN: 3030581500
Category : Computers
Languages : en
Pages : 678

View

Book Description
This book constitutes the proceedings of the 26th International Conference on Computing and Combinatorics, COCOON 2020, held in Atlanta, GA, USA, in August 2020. Due to the COVID-19 pandemic COCOON 2020 was organized as a fully online conference. The 54 papers presented in this volume were carefully reviewed and selected from 126 submissions. The papers cover various topics, including algorithm design, approximation algorithm, graph theory, complexity theory, problem solving, optimization, computational biology, computational learning, communication network, logic, and game theory.